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The values of λ for which one root of the equation x 2 + 1 - 2 λ x + λ 2 - λ - 2 = 0 is greater than 3 and the other smaller than 2 are given by

Options

  1. A2 < λ < 5
  2. B1 < λ < 4
  3. C1 < λ < 5
  4. D2 < λ < 4

Correct answer

D. 2 < λ < 4

Step-by-step solution

D &#62; 0 , &#160; f 2 &#60; 0 and f 3 &#60; 0 D = 1 - 2 &#955; 2 - 4 &#955; 2 - &#955; - 2 = 1 + 4 &#955; 2 - 4 &#955; - 4 &#955; 2 + 4 &#955; + 8 = 9 &#62; 0 (always true) f 2 &#60; 0 &#8658; 4 + 2 1 - 2 &#955; + &#955; 2 - &#955; - 2 &#60; 0 &#8658; 4 + 2 - 4 &#955; + &#955; 2 - &#955; - 2 &#60; - 0 &#8658; &#955; 2 - 5 &#955; + 4 &#60; 0 &#8658; &#955; &#8712; 1,4 ...(i) f 3 &#60; 0 &#8658; 9 + 3 1 - 2 &#955; + &#955; 2 - &#955; - 2 &#60; 0 &#8658; 9 + 3 - 6 &#955; + &#955; 2 - &#955; - 2 &#60; 0 &#8658; &#955;

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